To solve this equation, we'll first simplify the first expression:

-2 2/15 + 5/12

First, we need to convert the mixed number -2 2/15 into an improper fraction:
-2 2/15 = -[(2*15 + 2)/15] = -[32/15] = -32/15

Now we can add the fractions:
-32/15 + 5/12

To add these fractions, we need to find a common denominator, which is 60 in this case:
-32/15 = -324 / 154 = -128/60
5/12 = 55 / 125 = 25/60

Now we can add the fractions:
-128/60 + 25/60 = -103/60

Next, we'll simplify the second expression:

Finally, we'll subtract the third expression:

-3 11/12 = - 3 - 11/12 = -36/12 - 11/12 = -47/12

Therefore, putting it all together, our final answer is:
-103/60 + 2 - 47/12 = -103/60 + 120/60 - 47/12
= (120 - 103) / 60 - 47/12
= 17/60 - 47/12
= (175) / (605) - 47/12
= 85/300 - 47/12
= (85 - 141) / 300
= -56/300
= -14/75

So, the final answer is -14/75.